Question: Solve for $x$ and $y$ using elimination. ${6x+3y = 42}$ ${5x-3y = 13}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $11x = 55$ $\dfrac{11x}{{11}} = \dfrac{55}{{11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {6x+3y = 42}\thinspace$ to find $y$ ${6}{(5)}{ + 3y = 42}$ $30+3y = 42$ $30{-30} + 3y = 42{-30}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {5x-3y = 13}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ - 3y = 13}$ ${y = 4}$